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A003711 E.g.f. cos(tanh(x)) (even powers only).
(Formerly M4665)
4
1, -1, 9, -177, 6097, -325249, 24807321, -2558036145, 342232522657, -57569080467073, 11879658510739497, -2948163649552594737, 865683568087537789297, -296699416391356495667713, 117330699580950022391960505 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=0..14.

FORMULA

a(n) = sum(m=1..n, (sum(k=0..2*n-2*m, binomial(2*m+k-1,2*m-1)*(2*m+k)!*(-1)^(k)*2^(2*n-2*m-k)*Stirling2(2*n,2*m+k)))/(2*m)!), n>0, a(0)=1. - Vladimir Kruchinin, Jun 10 2011

MATHEMATICA

nn = 20; Table[(CoefficientList[Series[Cos[Tanh[x]], {x, 0, 2*nn}], x] * Range[0, 2*nn]!)[[n]], {n, 1, 2*nn+1, 2}] (* Vaclav Kotesovec, Feb 16 2015 *)

PROG

(Maxima)

a(n):=sum((sum(binomial(2*m+k-1, 2*m-1)*(2*m+k)!*(-1)^(k)*2^(2*n-2*m-k)*stirling2(2*n, 2*m+k), k, 0, 2*n-2*m))/(2*m)!, m, 1, n); /* Vladimir Kruchinin, Jun 10 2011 */

CROSSREFS

Sequence in context: A157774 A232694 A193443 * A009009 A220267 A034221

Adjacent sequences:  A003708 A003709 A003710 * A003712 A003713 A003714

KEYWORD

sign

AUTHOR

R. H. Hardin, Simon Plouffe

STATUS

approved

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Last modified February 23 17:23 EST 2018. Contains 299584 sequences. (Running on oeis4.)